Generalized Fejér–Hermite–Hadamard type via generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mrow><mml:mo>(</mml:mo><mml:mi>h</mml:mi><mml:mo linebreak="goodbreak">−</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math>-convexity on fractal sets and applications

In this article, we define a new class of convexity called generalized $(h-m)$-convexity, which generalizes $h$-convexity and $m$-convexity on fractal sets $\mathbb{R}^{\alpha}$ $(0<\alpha\leq 1)$. Some properties are discussed. Using local fractional integrals Hermite-Hadamard (H-H) Fej\'er-Hermite-Hadamard (Fej\'er-H-H) types inequalities. We also obtained result the Fej\'er-H-H type for function whose derivative in absolute value is $(h-m)$-convexity sets. applications to random variables numerical integrations studied.